Algebraic & Geometric Topology

Hopf algebras and invariants of the Johnson cokernel

Jim Conant and Martin Kassabov

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We show that if H is a cocommutative Hopf algebra, then there is a natural action of Aut(Fn) on Hn which induces an Out(Fn) action on a quotient Hn¯. In the case when H = T(V ) is the tensor algebra, we show that the invariant TrC of the cokernel of the Johnson homomorphism studied in Algebr. Geom. Topol. 15 (2015) 801–821 projects to take values in Hvcd(Out(Fn);Hn¯). We analyze the n = 2 case, getting large families of obstructions generalizing the abelianization obstructions of Geom. Dedicata 176 (2015) 345–374.

Article information

Algebr. Geom. Topol., Volume 16, Number 4 (2016), 2325-2363.

Received: 17 September 2015
Revised: 20 January 2016
Accepted: 24 January 2016
First available in Project Euclid: 28 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20J06: Cohomology of groups 16T05: Hopf algebras and their applications [See also 16S40, 57T05] 17B40: Automorphisms, derivations, other operators
Secondary: 20C15: Ordinary representations and characters 20F28: Automorphism groups of groups [See also 20E36]

Johnson homomorphism Hopf algebras automorphism groups of free groups


Conant, Jim; Kassabov, Martin. Hopf algebras and invariants of the Johnson cokernel. Algebr. Geom. Topol. 16 (2016), no. 4, 2325--2363. doi:10.2140/agt.2016.16.2325.

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